Don't tell him when your in labor and don't put him on the birth cirtificate
Well, my boyfriend has been in a similar situation. Not an abusive one or anything, but he feared for the safety of his kids whenever they went with their mother. He went to court to get full custody of the boys and that's what he based his case on. The fact that he feared for their safety. The only tricky part in YOUR situation is being able to prove that he's done something to make you think he would flee or try to harm the children in any way.
Long story short, my boyfriend never stopped the mother from seeing the boys, but she cannot take them out of the state or out of the area. She is supposed to see them the first Saturday of every month... (as determined by the court) but she has failed to do so anyway.
So, my advice to you is to find a way to prove why you fear for the safety of the kids being around him. Being abusive to you and fearing for the safety of your kids are two different topics in court. << IN COURT!!
Talk to some people, call a legal hotline maybe to get further advice on how you could go about making sure your children stay safe..
Good luck... Sorry you have to deal with this...